Abstract
We consider second order uniformly elliptic operators of divergence form in Rd + 1 whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators related with Poisson operators and Dirichlet–Neumann maps. Consequently, we obtain a solution formula for the inhomogeneous elliptic boundary value problem in the half space, which is useful to show the existence of solutions in a wider class of inhomogeneous data. We also establish L2 solvability of boundary value problems for a new class of the elliptic operators.
Original language | English |
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Pages (from-to) | 459-512 |
Number of pages | 54 |
Journal | manuscripta mathematica |
Volume | 152 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 2017 Mar 1 |
Keywords
- 35J15
- 35J25
ASJC Scopus subject areas
- Mathematics(all)